FMCW Radar

This is an FMCW radar simulation example based on RadarSimPy.

Radar Model

Transmitter

Setup the basic transmitter parameters through Transmitter module.

The following table lists the parameters in this example.

Parameter	Variable in Transmitter	Value
Frequency ($f$)	f	[24.075, 24.175] GHz
Time ($T$)	t	80e-6 s
Transmitted power ($P_t$)	tx_power	10 dBm
Pulse repetition period ($PRP$)	prp	100 us
Number of pulses	pulses	256

Here, f and t define the frequency modulation of the transmitter. The frequency changes from 24.075 GHz to 24.175 GHz within 80e-6 s.

import numpy as np
from radarsimpy import Radar, Transmitter, Receiver

tx_channel = dict(
    location=(0, 0, 0),
)

f_offset = np.arange(0, -743203072, -2903137)

prp = np.array([5.3302013e-05,5.3306039e-05,5.3310066e-05,5.3314094e-05,5.3318121e-05,5.332215e-05,5.3326178e-05,5.3330207e-05,5.3334237e-05,5.3338267e-05,5.3342298e-05,5.3346328e-05,5.335036e-05,5.3354392e-05,5.3358424e-05,5.3362457e-05,5.336649e-05,5.3370524e-05,5.3374558e-05,5.3378593e-05,5.3382628e-05,5.3386663e-05,5.3390699e-05,5.3394736e-05,5.3398773e-05,5.340281e-05,5.3406848e-05,5.3410886e-05,5.3414925e-05,5.3418964e-05,5.3423004e-05,5.3427044e-05,5.3431084e-05,5.3435125e-05,5.3439167e-05,5.3443209e-05,5.3447251e-05,5.3451294e-05,5.3455337e-05,5.3459381e-05,5.3463425e-05,5.346747e-05,5.3471515e-05,5.3475561e-05,5.3479607e-05,5.3483653e-05,5.34877e-05,5.3491748e-05,5.3495796e-05,5.3499844e-05,5.3503893e-05,5.3507942e-05,5.3511992e-05,5.3516042e-05,5.3520093e-05,5.3524144e-05,5.3528196e-05,5.3532248e-05,5.35363e-05,5.3540353e-05,5.3544407e-05,5.354846e-05,5.3552515e-05,5.355657e-05,5.3560625e-05,5.3564681e-05,5.3568737e-05,5.3572793e-05,5.3576851e-05,5.3580908e-05,5.3584966e-05,5.3589025e-05,5.3593084e-05,5.3597143e-05,5.3601203e-05,5.3605263e-05,5.3609324e-05,5.3613385e-05,5.3617447e-05,5.3621509e-05,5.3625572e-05,5.3629635e-05,5.3633699e-05,5.3637763e-05,5.3641827e-05,5.3645892e-05,5.3649958e-05,5.3654023e-05,5.365809e-05,5.3662157e-05,5.3666224e-05,5.3670292e-05,5.367436e-05,5.3678428e-05,5.3682498e-05,5.3686567e-05,5.3690637e-05,5.3694708e-05,5.3698779e-05,5.370285e-05,5.3706922e-05,5.3710994e-05,5.3715067e-05,5.371914e-05,5.3723214e-05,5.3727288e-05,5.3731363e-05,5.3735438e-05,5.3739514e-05,5.374359e-05,5.3747666e-05,5.3751743e-05,5.3755821e-05,5.3759899e-05,5.3763977e-05,5.3768056e-05,5.3772135e-05,5.3776215e-05,5.3780295e-05,5.3784376e-05,5.3788457e-05,5.3792539e-05,5.3796621e-05,5.3800704e-05,5.3804787e-05,5.380887e-05,5.3812954e-05,5.3817039e-05,5.3821123e-05,5.3825209e-05,5.3829295e-05,5.3833381e-05,5.3837468e-05,5.3841555e-05,5.3845643e-05,5.3849731e-05,5.3853819e-05,5.3857908e-05,5.3861998e-05,5.3866088e-05,5.3870178e-05,5.3874269e-05,5.3878361e-05,5.3882453e-05,5.3886545e-05,5.3890638e-05,5.3894731e-05,5.3898825e-05,5.3902919e-05,5.3907014e-05,5.3911109e-05,5.3915204e-05,5.3919301e-05,5.3923397e-05,5.3927494e-05,5.3931592e-05,5.393569e-05,5.3939788e-05,5.3943887e-05,5.3947986e-05,5.3952086e-05,5.3956186e-05,5.3960287e-05,5.3964388e-05,5.396849e-05,5.3972592e-05,5.3976695e-05,5.3980798e-05,5.3984901e-05,5.3989005e-05,5.399311e-05,5.3997215e-05,5.400132e-05,5.4005426e-05,5.4009532e-05,5.4013639e-05,5.4017747e-05,5.4021854e-05,5.4025963e-05,5.4030071e-05,5.403418e-05,5.403829e-05,5.40424e-05,5.4046511e-05,5.4050622e-05,5.4054733e-05,5.4058845e-05,5.4062958e-05,5.4067071e-05,5.4071184e-05,5.4075298e-05,5.4079412e-05,5.4083527e-05,5.4087642e-05,5.4091758e-05,5.4095874e-05,5.4099991e-05,5.4104108e-05,5.4108226e-05,5.4112344e-05,5.4116462e-05,5.4120581e-05,5.4124701e-05,5.4128821e-05,5.4132941e-05,5.4137062e-05,5.4141184e-05,5.4145305e-05,5.4149428e-05,5.4153551e-05,5.4157674e-05,5.4161798e-05,5.4165922e-05,5.4170046e-05,5.4174172e-05,5.4178297e-05,5.4182423e-05,5.418655e-05,5.4190677e-05,5.4194804e-05,5.4198932e-05,5.4203061e-05,5.420719e-05,5.4211319e-05,5.4215449e-05,5.4219579e-05,5.422371e-05,5.4227841e-05,5.4231973e-05,5.4236105e-05,5.4240238e-05,5.4244371e-05,5.4248505e-05,5.4252639e-05,5.4256774e-05,5.4260909e-05,5.4265044e-05,5.426918e-05,5.4273317e-05,5.4277454e-05,5.4281591e-05,5.4285729e-05,5.4289867e-05,5.4294006e-05,5.4298146e-05,5.4302285e-05,5.4306426e-05,5.4310566e-05,5.4314708e-05,5.4318849e-05,5.4322991e-05,5.4327134e-05,5.4331277e-05,5.4335421e-05,5.4339565e-05,5.4343709e-05])

tx = Transmitter(f=[76990079472.5000, 76750220463.5000],
                 t=4.92e-05,
                 f_offset=f_offset,
                 tx_power=10,
                 prp=prp,
                 pulses=256,
                 channels=[tx_channel])

Receiver

Setup the receiver parameters through Receiver module.

The parameters of the receiver are listed in the table below.

Parameter	Variable in Receiver	Value
Sampling rate ($f_s$)	fs	2 Msps
Noise figure ($NF$)	noise_figure	12 dB
RF gain/loss ($G_{rf}$)	rf_gain	20 dB
Load resistor ($R_L$)	load_resistor	500 $\Omega$
Baseband voltage gain ($G_{BB}$)	baseband_gain	30 dB

rx_channel = dict(
    location=(0, 0, 0),
)

rx = Receiver(fs=20e6,
              noise_figure=12,
              rf_gain=20,
              load_resistor=500,
              baseband_gain=30,
              channels=[rx_channel])

Create the FMCW radar model based on all the parameters defined above.

radar = Radar(transmitter=tx, receiver=rx)

Calculate the characteristics of the FMCW radar:

• Maximum range (with I/Q baseband): $$R_{max}=\frac{c f_s T}{2B}$$

• Maximum range (without I/Q baseband): $$R_{max}=\frac{c f_s T}{4B}$$

• Unambiguous velocity: $$v_{ua}=\frac{c}{2 CRP \times f_c}$$ or $$v_{ua}=\pm \frac{c}{4 CRP \times f_c}$$

• Range resolution: $$\delta_r=\frac{c}{2B}$$

print('Maximum range: ', radar.max_range, ' m')
print('Maximum unambiguous speed: ', radar.unambiguous_speed, ' m/s')
print('Range_resolution: ', radar.range_resolution, ' m')

Maximum range:  614.9357906168952  m
Maximum unambiguous speed:  36.58384666012473  m/s
Range_resolution:  0.6249347465618854  m

Targets

The propertities of targets are defined here. There are 3 targets in this simulation. The locations of the targets are defined through $(x, y, z)$ coordinates in meters, and the speeds of the targets are defined trough $(v_x, v_y, v_z)$ in $m/s$. The propertites of the targets also includes radar cross-section (RCS (dBsm)) and phase (degree).

target_1 = dict(location=(60, 0, 0), speed=(-20, 0, 0), rcs=20, phase=0)

targets = [target_1]

Simulate Baseband Signals

Use the simulator module to simulate the baseband samples. The user can choose between Python engine simpy or C++ engine simc.

The output baseband data is a 3-D matrix:

$[channels, pulses, ADC~samples]$

# Python engine
from radarsimpy.simulator import simpy
# C++ engine
from radarsimpy.simulator import simc

bb_data = simc(radar, targets, noise=False)
time_matrix = bb_data['timestamp']
data_matrix = np.real(bb_data['baseband'])

Plot the baseband samples

import plotly.graph_objs as go
from IPython.display import SVG, display

fig = go.Figure()

fig.add_trace(go.Scatter(
    x=time_matrix[0, 0, :],
    y=np.real(data_matrix[0, 0, :]),
    name='I',
))
fig.add_trace(go.Scatter(
    x=time_matrix[0, 0, :],
    y=np.imag(data_matrix[0, 0, :]),
    name='Q',
))

fig.update_layout(
    title='I/Q Baseband Signals',
    yaxis=dict(title='Amplitude (V)'),
    xaxis=dict(title='Time (s)'),
)

# fig.show()
display(SVG(fig.to_image(format='svg', scale=1)))

Radar Signal Processing

Range profile

from scipy import signal
import radarsimpy.processing as proc

range_window = signal.chebwin(radar.samples_per_pulse, at=60)
range_profile = proc.cal_range_profile(radar, data_matrix, range_window, n=1024)

Plot range profiles

range_axis = np.linspace(
    0, radar.max_range, radar.samples_per_pulse, endpoint=False)

doppler_axis = np.linspace(
    0, radar.transmitter.pulses, radar.transmitter.pulses, endpoint=False)

fig = go.Figure()

fig.add_trace(go.Surface(x=range_axis, y=doppler_axis, z=20 *
              np.log10(np.abs(range_profile[0, :, :])), colorscale='Rainbow'))

fig.update_layout(
    title='Range Profile',
    height=600,
    scene=dict(
        xaxis=dict(title='Range (m)'),
        yaxis=dict(title='Chirp'),
        zaxis=dict(title='Amplitude (dB)'),
        aspectmode='cube',
    ),
)

# fig.show()
display(SVG(fig.to_image(format='svg', scale=1)))

Range-Doppler processing

doppler_window = signal.chebwin(radar.transmitter.pulses, at=60)
range_doppler = proc.cal_range_doppler(
    radar, range_profile, doppler_window, fft_shift=False)

Plot range-Doppler map

range_axis = np.arange(0, 1024, 1)

doppler_axis = np.arange(0, 256, 1)

fig = go.Figure()
fig.add_trace(go.Surface(x=range_axis, y=doppler_axis, z=20 *
              np.log10(np.abs(range_doppler[0, :, :])), colorscale='Rainbow'))

fig.update_layout(
    title='Range Doppler',
    height=600,
    scene=dict(
        xaxis=dict(title='Range (m)'),
        yaxis=dict(title='Velocity (m/s)'),
        zaxis=dict(title='Amplitude (dB)'),
        aspectmode='cube',
    ),
)

fig.show()
# display(SVG(fig.to_image(format='svg', scale=1)))